Still it was the largest among the empires that rose in India
I am going to say that with modern scholarship in mind it is a disingenuous argument to claim that the Mauryas had a larger state than the current Republic and probably the Mughals.[1] According to recent research the Mauryan state was a 'spider,' a very decentralized state - the Mughals most likely held
effective control over more land, at least briefly during Aurangzeb, and the current Republic definitely does.
The geography of Mauryan empire resembled a spider with a small dense body and long spindly legs.The highest echelons of imperial society lived in the inner circle composed of the ruler, his immediate family, other relatives, and close allies, who formed a dynastic core. Outside the core, Mauryan empire ran along stringy routes dotted with armed cities. (from India and South Asia: A Short History)
In other words, Magadha, the Gangetic imperial core or the 'head of the spider,' was most likely quite centralized and fairly uniformly administered. Central authority in territories surrounding this core was significant, but not as strong as in Magadha itself. Outside the northern heartland, imperial control was limited, with imperial control very possibly present only in major roads and resource-producing areas like the gold mines of Karnataka. To quote "The First Millennium B.C. in Northern India" by Romila Thapar that I've been drawing on,
Excavations carried out so far at sites close to the location of Asokan inscriptions, do not provide significant evidence of a Mauryan presence. Asokan inscriptions tend to cluster in Karnataka. The archaeological sites are largely those of megalithic burials and settlements, suggesting that there was a pre-existing pattern of habitation and exchange into which the Mauryas may have intruded [...] Mauryan control seems to have been greater in those areas where they were tapping resources, as, for example, gold, and hence the cluster of inscriptions. Possibly, other resources were obtained through local agencies, such as the people inhabiting the megalithic sites, and their way of life remained substantially unchanged by the Mauryan presence.
Archaeologically there's no real 'Mauryan ceramic phase,' for example.
To sum up things by quoting "Imperial Landscapes of South Asia" by Carla M. Sinopoli,
While the Mauryans may have had effective territorial control in their northern heartland, imperial territories in Peninsular India were restricted to areas near important mineral resources and trade routes, suggesting discontinuous territories and limited presence in many areas of the peninsula. Other than the inscriptions and some rare artifacts, areas distant from the imperial core contain relatively little direct evidence of the Mauryan presence, and no evidence of the form that presence may have taken.
That is, I am partial to the following map of the Mauryan empire (taken from Sinopoli, "Imperial Landscapes") than those on Wikipedia:
[1] Who did not, by the way, rise in India as you state; Babur was born and crowned in Andijan and reigned as ruler of Kabul much longer than as ruler of Hindustan, and in a broader sense the Mughals were Timurids.