A collection of 1,586,354 Church of England Hampshire parish register entries of births and baptisms running between 1813 and 1921 briefly appeared, then disappeared on Ancestry. Alphabetically the parishes range from Abbotts Ann to Yateley, including 17 Bournemouth and 14 Winchester parishes – those for Southampton are lacking.
The records, from the Hampshire Record Office, were name searchable with links to the originals which were browsable.
What happenned? They may be back by the time you see this.
In the meantime, Findmypast has over 600 thousand transcript records for baptisms from the Hampshire Genealogical Society. FamilySearch has over 2 million parish register entries and Bishops transcripts for BMBs of all types with transcriptions viewable for registered readers and images viewable at FSCs and affiliate libraries.