How big will the believer’s dominion be in Paradise? What deeds could increase the size of his dominion?

Allah, may He be exalted, has prepared Paradise for His pious
slaves and has made its breadth like the breadth of heaven and earth, which
is indicative of its vastness and great size. Allah, may He be exalted, will
honour His slaves therein by His grace and mercy, and His grace is immense
and His mercy is vast. Part of that honour is the great dominion that the
people of Paradise will have. Allah, may He be exalted, says, describing
that (interpretation of the meaning): “And when you look there (in
Paradise), you will see a delight (that cannot be imagined), and a great
dominion” [al-Insaan 76:20]. 

In the saheeh Sunnah there is a description of the abundance
that the lowest of the people of Paradise in status will have, which is ten
times this world! So how about the highest of them in status? It was
narrated from ‘Abdullah ibn Mas‘ood (may Allah be pleased with him) that the
Prophet (blessings and peace of Allah be upon him) said: “I know the last of
the people of Hell to be brought forth, and the last of the people of
Paradise to enter therein. It will be a man who will emerge crawling from
Hell, and Allah will say to him: ‘Go and enter Paradise.’ He will come to it
and it will appear to him to be full. He will go back and say, ‘O Lord, I
found it full.’  Allah, may He be blessed and exalted, will say to him: ‘Go
and enter Paradise.’ He will go to it and it will appear to him to be full.
He will go back and say, ‘O Lord, I found it full.’ Allah, may He be blessed
and exalted, will say to him: ‘Go and enter Paradise, and you will have the
equivalent of the whole world and ten times as much.’ He will say, ‘Are You
mocking me – or laughing at me – when You are the Sovereign?’” He said: And
I saw the Messenger of Allah (blessings and peace of Allah be upon him)
smile so broadly that his molars appeared. And he used to say: “That will be
the lowest of the people of Paradise in status.”

Narrated by al-Bukhaari (6202); Muslim (186). 

With regard to deeds and acts of obedience that the Muslim
can do to increase the size of his dominion in Paradise, we do not know of
anything proven in the Sunnah. But undoubtedly if the Muslim has a space in
Paradise the size of a whip or the size of a bow, that will be better for
him than this world and everything in it, as is narrated in a saheeh report
from the Prophet (blessings and peace of Allah be upon him). It was narrated
that Sahl ibn Sa‘d as-Saa‘idi said: The Messenger of Allah (blessings and
peace of Allah be upon him) said: “The space of the whip of one of you in
Paradise is better than this world and everything in it.” Narrated by al-Bukhaari
(2735). And it was narrated from Abu Hurayrah (may Allah be pleased with
him) that the Prophet (blessings and peace of Allah be upon him) said: “The
short span of the bow of one of you in Paradise is better than that on which
the sun rises or sets.” Narrated by al-Bukhaari (2643). 

The “short span” of a bow is the area between the middle
(where the archer grasps it) and the end of the bow. What is meant is that
the space of that size in Paradise is better than this world and everything
in it. And the same is said concerning the space of a whip. 

It is proven in the saheeh Sunnah that the tent of the
believer in Paradise will be sixty miles long, so how big will the size of
his dominion be if that is the length of just one tent? It was narrated from
Abu Moosa al-Ash‘ari (may Allah be pleased with him) that the Prophet
(blessings and peace of Allah be upon him) said: “In Paradise the believer
will have a tent made from a single hollowed-out pearl, sixty miles long, in
which the believer will have wives and he will go around among them and they
will not see one another.”

Narrated by al-Bukhaari (4598) and Muslim (2838); according
to another version it is “sixty miles wide”. 

And Allah knows best.