Which division is responsible for maintaining the register of property owners?

The parish assessor's office is responsible for maintaining the register of property owners. This office plays a critical role in property valuation and assessment for tax purposes, which requires accurate and up-to-date records of property ownership. By keeping a detailed register, the assessor can determine property values and ensure that taxes are levied fairly based on ownership and property characteristics.

The other options would not typically manage the property ownership register. The parish lawyer’s office focuses on legal matters and representation for the parish, the parish tax collector’s office deals primarily with collecting taxes, and the parish land office usually pertains to land use, zoning, or conveyancing, rather than maintaining ownership records. Therefore, the parish assessor's office is uniquely aligned with the responsibilities of maintaining the register of property owners, ensuring that comprehensive records are accessible for assessment and taxation purposes.